The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers?

Correct Answer: ³⁄₄

Explanation:

1400 x x = 1050   ⟹   x =	1050	=	3
	1400		4

Correct Answer: 202860

Explanation:

45 = 5 x 9, where 5 and 9 are co-primes.

Unit digit must be 0 or 5 and sum of digits must be divisible by 9.

Among given numbers, such number is 202860.

Correct Answer: 10

Explanation:

 4 a 3  |
 9 8 4  }  ==> a + 8 = b  ==>  b - a = 8  
13 b 7  |

Also, 13 b 7 is divisible by 11   ⟹   (7 + 3) - ( b + 1) = (9 - b )

⟹   (9 - b) = 0

⟹   b = 9

∴ (b = 9 and a = 1)    ⟹ (a + b) = 10.

Correct Answer: 4155

Explanation:

Let 7589 -x = 3434

Then, x = 7589 - 3434 = 4155

Correct Answer: 1765113

Explanation:

Let 4300731 - x = 2535618

Then x, = 4300731 - 2535618 = 1765113

Correct Answer: 578

Explanation:

Given Exp. =	(a3 - b3)	= (a - b) = (854 - 276) = 578
	(a2 + ab + b2)

Correct Answer: 1035

Explanation:

Let S _n = (1 + 2 + 3 + ... + 45)

This is an A.P. in which a = 1, d = 1, n = 45 and l = 45

∴Sn =	n	(a + l)	=	45	x (1 + 45)   = (45 x 23)   = 1035
	2			2

Required sum = 1035.

Correct Answer: 2

Explanation:

Let n = 4 q + 3. Then 2 n = 8 q + 6   = 4(2 q + 1 ) + 2.

Thus, when 2n is divided by 4, the remainder is 2.

Correct Answer: 9

Explanation:

Unit digit in (4137) ⁷⁵⁴ = Unit digit in {[(4137) ⁴ ] ¹⁸⁸ x (4137) ² }

=Unit digit in { 292915317923361 x 17114769 }

= (1 x 9) = 9

Correct Answer: 150

Explanation:

3-digit number divisible by 6 are: 102, 108, 114,... , 996

This is an A.P. in which a = 102, d = 6 and l = 996

Let the number of terms be n. Then t_n = 996.

∴ a + (n - 1)d = 996

⟹ 102 + (n - 1) x 6 = 996

⟹ 6 x (n - 1) = 894

⟹ (n - 1) = 149

⟹ n = 150

∴ Number of terms = 150.